A Nested Differential Evolution Algorithm for Optimal Designs of Quantile Regression Models

Abstract

The Differential Evolution (DE) is an influential heuristic algorithm effective in attaining global optimization of any real vector-valued function. Easy to construct and use, this algorithm is increasingly popular in the field of solving complex optimization problems without any assumptions about the objective function. This article outlines the fundamental DE algorithm and subsequently proposes a nested DE algorithm to address the issue of finding the maximin optimal designs in quantile regression models. This algorithm can effectively address the issue of premature convergence and local optimum in many current theories and algorithms when searching for the maximin optimal designs of quantile regression. The proposed algorithm was applied to common dose response models, including the Michaelis-Menten model, Emax model, and Exponential model, with multiple sets of experiments conducted to analyze the impact of different parameters and connection functions on the algorithm’s performance. The numerical results obtained from these experiments suggest that the algorithm can be applied to a number of complex models and the maximin optimal design of the quantile regression model can be effectively obtained.